Dr. Tirthankar Dasgupta, Professor and Co-Graduate Director
Department of Statistics, Rutgers University

Abstract:  D-Optimal designs for estimating parameters of response models are derived by maximizing the determinant of the Fisher information matrix. For non-linear models, the Fisher information matrix depends on the unknown parameter vector of interest, leading to a weird situation that in order to obtain the D-optimal design, one needs to have knowledge of the parameter to be estimated. One solution to this problem is to choose the design points sequentially, optimizing the D-optimality criterion using parameter estimates based on available data, followed by updating the parameters estimates using maximum likelihood estimation. On the other hand, there are many non-linear models for which closed-form results for D-optimal designs are available, but because such solutions involve the parameters to be estimated, they can only be used by substituting “guestimates” of parameters. In this paper, a hybrid sequential strategy called PICS (Plug into closed-form solution) is proposed that replaces the optimization of the objective function at every single step by plugging in the estimates into the available closed form solutions. Convergence of the sequence of solutions generated by the PICS approach to the true D-optimal solution, and asymptotic normality of the sequence of estimators generated by this approach are established. Usefulness of this approach in terms of saving computational time and achieving greater efficiency of estimation compared to the standard sequential approach are demonstrated with simulations conducted from two different sets of models motivated by real-life scenarios.